Consider the following.

$$cos$3($x$)$ sin$4($x$)$ dx

Which of the following are true?

The power of cosine is odd and positive. The power of sine is odd and positive.$$ The powers of both sine and cosine are even and nonnegative.

Which of the following guidelines can be applied to find this indefinite integral?

Save one sine factor and convert the remaining factors to cosines. Save one cosine factor and convert the remaining factors to sines.$$ Make repeated use of the formulas

sin$2($x$)=$

$1$ cos$(2$x$)2$

$$ and $$ cos$2($x$)=$

$1+$ cos$(2$x$)2$

to convert the integrand to odd powers of the cosine. Then proceed as in the second guideline.

Find the indefinite integral. $($Remember the constant of integration.$)$

$$cos$3($x$)$ sin$4($x$)$ dx $=$